A jury on Monday found Stevens, 84, guilty on seven counts of trying to hide more than $250,000 in free home renovations and other gifts that he received from a wealthy oil contractor. He has asked his Senate colleagues as well as Alaska's voters to stand by him as he appeals the convictions.
Palin, who had supported Stevens during his long career in Alaska politics, told CNBC that Stevens should do "the right thing."
"Ted Stevens, you know, a sad day for Alaska yesterday when he was found guilty of seven felonies," Palin said. "But - and now he needs to do the right thing, and the right thing is - as he's proclaiming his innocence and proclaiming, too, that he will go through the appellate process, OK, then he needs to step aside and allow our state to elect someone who will be supportive of those ideals of America: the free enterprise, the missions that we're on, to win the war, those things that have got to take place in order to progress this country. Ted Stevens has got to play a very statesmanlike role in this now."
Following the interview, the McCain campaign issued a statement by Palin in which she said she hoped that Stevens "would take the opportunity to do the statesmanlike thing and erase the cloud that is covering his Senate seat."
"He has not done so," she added. "Alaskans are grateful for his decades of public service, but the time has come for him to step aside. Even if elected on Tuesday, Sen. Stevens should step aside to allow a special election to give Alaskans a real choice of who will serve them in Congress."
A senator since 1968, Stevens faces re-election next week as a convicted felon. He could be sentenced to as many as 35 years in prison, but he was not expected to receive a harsh sentence. However, the Senate could expel Stevens even if he is re-elected.
In a statement issued by his campaign, McCain said the convictions were "a sign of the health of our democracy that the people continue to hold their representatives to account for improper or illegal conduct, but this verdict is also a sign of the corruption and insider-dealing that has become so pervasive in our nation's capital."
"It is clear that Sen. Stevens has broken his trust with the people and that he should now step down," McCain said. "I hope that my colleagues in the Senate will be spurred by these events to redouble their efforts to end this kind of corruption once and for all."
McCain and Stevens often clashed over so-called "earmarks," appropriations inserted into bills by senators seeking to fund home-state projects. McCain has opposed earmarks - he has cited them as a source of political corruption - while Stevens has proudly pointed to the billions of dollars in pork-barrel spending he has garnered for Alaska.
McCain's rival, Democrat Barack Obama, also held out Stevens' conviction as an example of what's wrong with Washington, and called for his resignation.
"Yesterday's ruling wasn't just a verdict on Senator Stevens but on the broken politics that has infected Washington for decades," said Obama. "It's time to put an end to the corruption and influence-peddling, restore openness and accountability, and finally put government back in the hands of the people it serves. Senator Stevens should step down."